Short answer: load the PDF, drag boxes over the text to remove, then redact. The pages you mark are rebuilt as images at the chosen resolution, so the characters are gone. Pages without a box are copied untouched and stay searchable.
Why this is different from drawing a rectangle
A PDF keeps its text in content streams, separate from whatever is drawn on top. A black rectangle is just another object painted later — the string underneath is untouched and comes back with a copy-paste. Rendering the page and drawing the boxes into the pixels is the only client-side way to make the removal real, and it is why the output pages lose their text layer.
Check the result before you send it
Open the downloaded file and try to select the redacted area. Nothing should highlight. The second check is to look for the value in a text search: it should not be found anywhere in the document, including the metadata — use the metadata remover as well when the name also appears in the author field.